Basic Math Examples

$(x + \frac{1}{3}) (x - \frac{2}{3})$

Step 1

Expand $(x + \frac{1}{3}) (x - \frac{2}{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x (x - \frac{2}{3}) + \frac{1}{3} (x - \frac{2}{3})$

Step 1.2

Apply the distributive property.

$x \cdot x + x (- \frac{2}{3}) + \frac{1}{3} (x - \frac{2}{3})$

Step 1.3

Apply the distributive property.

$x \cdot x + x (- \frac{2}{3}) + \frac{1}{3} x + \frac{1}{3} (- \frac{2}{3})$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

$x^{2} + x (- \frac{2}{3}) + \frac{1}{3} x + \frac{1}{3} (- \frac{2}{3})$

Step 2.1.2

Combine $x$ and $\frac{2}{3}$ .

$x^{2} - \frac{x \cdot 2}{3} + \frac{1}{3} x + \frac{1}{3} (- \frac{2}{3})$

Step 2.1.3

Move $2$ to the left of $x$ .

$x^{2} - \frac{2 \cdot x}{3} + \frac{1}{3} x + \frac{1}{3} (- \frac{2}{3})$

Step 2.1.4

Combine $\frac{1}{3}$ and $x$ .

$x^{2} - \frac{2 x}{3} + \frac{x}{3} + \frac{1}{3} (- \frac{2}{3})$

Step 2.1.5

Multiply $\frac{1}{3} (- \frac{2}{3})$ .

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Step 2.1.5.1

Multiply $\frac{1}{3}$ by $\frac{2}{3}$ .

$x^{2} - \frac{2 x}{3} + \frac{x}{3} - \frac{2}{3 \cdot 3}$

Step 2.1.5.2

Multiply $3$ by $3$ .

$x^{2} - \frac{2 x}{3} + \frac{x}{3} - \frac{2}{9}$

Step 2.2

Combine the numerators over the common denominator.

$x^{2} + \frac{- 2 x + x}{3} - \frac{2}{9}$

Step 3

Add $- 2 x$ and $x$ .

$x^{2} + \frac{- x}{3} - \frac{2}{9}$

Step 4

Move the negative in front of the fraction.

$x^{2} - \frac{x}{3} - \frac{2}{9}$